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^{+0}
235031 Questions
0
10
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+2653
Number Theory
You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from
read more ..
LiIIiam0216
Aug 5, 2024
0
6
0
+398
Number Theory
When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
0.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.
When
read more ..
cooIcooIcooI17
Aug 5, 2024
+1
7
1
+24
Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $10$ positive divisors, and $mn$ has exactly
Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $10$ positive divisors, and $mn$ has exactly $22$ positive divisors, then how many divisors does $m^2 n^2$ have?
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dogsrule
Aug 5, 2024
Aug 4, 2024
0
7
0
+398
Number Theory
Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.
cooIcooIcooI17
Aug 4, 2024
0
7
0
+398
Number Theory
Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.
cooIcooIcooI17
Aug 4, 2024
0
9
0
+1234
Number Theory
On planet Enigma, the residents use a currency called the confusion. There are only 2 confusion bills on Enigma, one worth 2 confusions and the other worth 3 confusions. There are also some coins of smaller value, but each weighs over 10
read more ..
Akhain1
Aug 4, 2024
0
5
1
+2653
Number Theory
The product of a set of distinct positive integers is $630$. If one of the numbers is 42, what are the other two numbers?
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LiIIiam0216
Aug 4, 2024
0
8
0
+1752
Number Theory
How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{24}?$
ABJeIIy
Aug 4, 2024
0
5
1
+904
Geometry
In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?
●
Rangcr897
Aug 4, 2024
+2
7
1
+19
Probability
Three fair quarters are tossed, and a tail appears on at least one of them. What is the probability that at least one head appears? Express your answer as a common fraction.
●
DeluluSunshine
Aug 4, 2024
0
6
0
+802
Algebra
Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x)$ and $y=f(x^3)$ are drawn, at how many points do they intersect?
RedDragonl
Aug 4, 2024
0
8
0
+802
Algebra
Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?
RedDragonl
Aug 4, 2024
0
5
1
+802
Algebra
The parabola $y = ax^2 + bx + c$ is graphed below. Find $a \cdot b \cdot c.$ (The grid lines are one unit apart.)
read more ..
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RedDragonl
Aug 4, 2024
0
5
1
+802
Algebra
The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a.
read more ..
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RedDragonl
Aug 4, 2024
0
1
1
+904
Geometry
In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
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Rangcr897
Aug 4, 2024
0
7
1
+559
Algebra
Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.
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siIviajendeukie
Aug 4, 2024
0
3
1
+559
Algebra
Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions
●
siIviajendeukie
Aug 4, 2024
0
4
1
+2653
Algebra
The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?
●
LiIIiam0216
Aug 4, 2024
0
8
1
+2653
Algebra
Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.
●
LiIIiam0216
Aug 4, 2024
0
6
1
+2653
Algebra
Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator
read more ..
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LiIIiam0216
Aug 4, 2024
0
7
1
+613
help algebra
The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?
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gnistory
Aug 4, 2024
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